Data:
Loan=$278 at 10%
A simple interest is calculated for payments on the initial capital.
If the total interest was $174.12.
If the interest is on a year. You calculated the interes of one year. The 10% of $278:
[tex]278\cdot\frac{10}{100}=27.8[/tex]In a year the interest is $27.8.
Then, $174.12 divided into $27.8 is the number of years of the loan:
[tex]\frac{174.12}{27.8}=6.26\approx6[/tex]Then, the loan was for 6 years